This surface was suggested by S. Mukai [1]}.
First we give a definition of the dual graph of type \(\Gamma _{\rm MI}\) .
We denote by \((ij)\)  the transposition of \(i\)  and \(j\) 
(\(1 \le i < j \le 6\) ) which is classically called Sylvester's duad.
Six letters \(1,2,3,4,5,6\)  can be arranged in three pairs of duads,
for example, \((12, 34, 56)\) , called Sylvester's syntheme
(it is understood that \((12, 34, 56)\)  is the same as \((12, 56, 34)\)  or \((34, 12, 56)\) ).
Duads and synthemes are in \((3,3)\)  correspondence, that is, each syntheme consists
of three duads and each duad belongs to three synthemes (see [2]}).
A triad \((ijk)\)  is a subset of \(\lbrace 1,2,3,4,5,6\rbrace \)  of cardinality 3, up to complementary set. There are ten triads.
